New stabilizer codes with parameters better than the ones available in the
literature are provided in this work, in particular quantum codes with
parameters [[127,63,≥12]]2 and [[63,45,≥6]]4 that are records.
These codes are constructed with a new generalization of the Steane's
enlargement procedure and by considering orthogonal subfield-subcodes --with
respect to the Euclidean and Hermitian inner product-- of a new family of
linear codes, the J-affine variety codes